Geodesic
Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion
Kybernetika, Tome 34 (1998) no. 2, p. [217].

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We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations $x_{t+1}=F(x_t,a_t,\xi _t),\,\,t=0,1,\ldots $ with i.i.d. $\Re ^k$-valued random vectors $\xi _t$ whose density $\rho $ is unknown. Assuming observability of $\xi _t$ we propose the procedure of statistical estimation of $\rho $ that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded costs.
Classification : 60J05, 62M05, 93C40, 93E35
Keywords: Markov control process; unbounded costs; discounted asymptotic optimality; density estimator; rate of convergence 
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     author = {Gordienko, Evgueni I. and Minj\'arez-Sosa, J. Adolfo},
     title = {Adaptive control for discrete-time {Markov} processes with unbounded costs: {Discounted} criterion},
     journal = {Kybernetika},
     pages = {[217]},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {1998},
     mrnumber = {1621512},
     zbl = {1274.90474},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998__34_2_a8/}
}
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Gordienko, Evgueni I.; Minjárez-Sosa, J. Adolfo. Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion. Kybernetika, Tome 34 (1998) no. 2, p. [217]. http://geodesic.mathdoc.fr/item/KYB_1998__34_2_a8/